I posted a full rebuttal of the ' Moon landing was fake' theory on here a year or two ago. But the main point is that the 'space race' between the USSR and USA was really an arms race, all about who could develop the biggest missiles and get an advantage in a nuclear war.
The USSR constantly beat the USA in the 'space race' .
First satellite 'Sputnik 1 ' USSR. First animal in space USSR .
When the USSR launched Uri Gagarin into a full multi orbital space flight it was a hammer-blow to the USA. They were years behind and knew it. The conclusion was obvious. If the USSR could had a rocket powerful enough to launch a manned capsule into orbit and then bring it down where they wanted it, they could launch a warhead into orbit and bring it down in the USA ! That meant that they could hit the USA by surprise, at that time there was no way to track an object in Earth orbit.
The USA went into full panic mode, they strapped Alan Sheppard onto the top of the biggest missile they had and launched him into a sub orbital 'hop'. Until then the USA had been concentrating on the Bell 'X' series of rocket powered aircraft to get into space. (Sheppard's capsule was actually a modified cockpit from an 'X' craft.)
The 'X' craft project was hastily abandoned and resources put into pure rockets.
When the Apollo project took off it finally turned the tables on the USSR who were bitterly jealous, and watched every move in a hope they could discredit the USA . Even the smallest slip by the USA would have been a political windfall to the USSR, that is why the Moon landings could never be anything but 100% genuine.